Solve 1/3x-1/2leqx+5/6

$$\frac { 1 } { 3 } x - \frac { 1 } { 2 } \leq x + \frac { 5 } { 6 }$$

Solve for x

$$x\geq -2$$

Solution Steps

Subtract x from both sides.

$$\frac{1}{3}x-\frac{1}{2}-x\leq \frac{5}{6}$$

Combine \frac{1}{3}x and -x to get -\frac{2}{3}x.

$$-\frac{2}{3}x-\frac{1}{2}\leq \frac{5}{6}$$

Add \frac{1}{2} to both sides.

$$-\frac{2}{3}x\leq \frac{5}{6}+\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{2}{3}x\leq \frac{5}{6}+\frac{3}{6}$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}x\leq \frac{5+3}{6}$$

Add 5 and 3 to get 8.

$$-\frac{2}{3}x\leq \frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}x\leq \frac{4}{3}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}. Since -\frac{2}{3} is negative, the inequality direction is changed.

$$x\geq \frac{4}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{4}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{4\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{3\times 2}.

$$x\geq \frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$x\geq -2$$